Per the nginx documentation (emphasis mine):
What happens is that when nginx receives the HUP signal, it tries to parse the configuration file (the specified one, if present, otherwise the default), and if successful, tries to apply a new configuration (i.e. re-open the log files and listen sockets). If successful, nginx runs new worker processes and signals graceful shutdown to old workers. Notified workers close listen sockets but continue to serve current clients. After serving all clients old workers shutdown. If nginx couldn’t successfully apply the new configuration, it continues to work with an old configuration.
Thus, if you have a properly set up nginx configuration and yet you are still getting the default “Welcome to nginx!” page over and over, try restarting nginx itself. I wished I’d have realized this aspect of nginx before spending hours scratching my head.